Simplify the following expression: $ k = \dfrac{x - 3}{-2x} - \dfrac{9}{2} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{x - 3}{-2x} \times \dfrac{2}{2} = \dfrac{2x - 6}{-4x} $ Multiply the second expression by $\dfrac{-2x}{-2x}$ $ \dfrac{9}{2} \times \dfrac{-2x}{-2x} = \dfrac{-18x}{-4x} $ Therefore $ k = \dfrac{2x - 6}{-4x} - \dfrac{-18x}{-4x} $ Now the expressions have the same denominator we can simply subtract the numerators: $k = \dfrac{2x - 6 + 18x }{-4x} $ Distribute the negative sign: $k = \dfrac{2x - 6 + 18x}{-4x}$ $k = \dfrac{20x - 6}{-4x}$ Simplify the expression by dividing the numerator and denominator by -2: $k = \dfrac{-10x + 3}{2x}$